Mean-field theory for the inverse Ising problem at low temperatures

H. Chau Nguyen; Johannes Berg

doi:10.1103/physrevlett.109.050602

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arXiv · 1204.5375

Mean-field theory for the inverse Ising problem at low temperatures

H. Chau Nguyen·Johannes Berg

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Abstract

The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of spin configurations sampled from the Boltzmann measure. To invert the relationship between model parameters and observables (magnetisations and correlations) mean-field approximations are often used, allowing to determine model parameters from data. However, all known mean-field methods fail at low temperatures with the emergence of multiple thermodynamic states. Here we show how clustering spin configurations can approximate these thermodynamic states, and how mean-field methods applied to thermodynamic states allow an efficient reconstruction of Ising models also at low temperatures.

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BibTeX RIS

H. Chau Nguyen, Johannes Berg. 2012-04-24. Mean-field theory for the inverse Ising problem at low temperatures. https://doi.org/10.1103/physrevlett.109.050602

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